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Article Excerpt
This article develops a two-factor structural mortgage pricing model in which rational mortgage-holders choose when to prepay and default in response to changes in both interest rates and house prices. We estimate the model using comprehensive data on the pool-level termination rates for Freddie Mac Participation Certificates issued between 1991 and 2002. The model exhibits a statistically and economically significant improvement over the nested one-factor (interest-rate only) model in its ability to match historical prepayment data. Moreover, the two-factor model produces origination prices that are significantly closer to those quoted in the to-be-announced market than the one-factor model. Our results have important implications for hedging mortgage-backed securities.
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The residential mortgage-backed security (MBS) market is one of the largest and fastest-growing bond markets in the United States. (1) Valuing and hedging MBS requires a model for both the prepayment and default behavior of the underlying mortgages. While our understanding of this behavior has improved dramatically over the last two decades, significant challenges still remain. These challenges include, for example, the persistence of model-based MBS pricing errors (quantified in terms of the option-adjusted spread, or OAS), and the need for improved hedging strategies demonstrated by the sizable losses on MBS positions incurred by Askin Capital Management in the early 1990s and by Fannie Mae's recent problems with a large negative duration gap in its portfolio. (2) Further, for firms that participate in the MBS market, recent changes in accounting standards now require firms to account for hedging effectiveness directly on the income statement, raising the visibility of any hedging mistakes. (3)
Some of these problems stem, at least in part, from the widespread use of models for pricing and hedging MBS that focus principally on the effect of interest rates on mortgage prepayment. While interest rates are generally acknowledged to be the most important factor affecting prepayment, there is a substantial literature suggesting that house prices also play an important role. For example, Stein (1995), Archer, Ling and McGill (1996), Mayer and Genesove (1997) and Mattey and Wallace (1998, 2001) emphasize the importance of housing prices as a determinant of regional-level household mobility. To the extent that declines in house prices impinge on borrowers' mobility, housing turnover and hence prepayments would fall. In a similar vein, Longstaff (2004) suggests that declining house prices reduce refinancing activity by impairing borrowers' credit quality, thereby hurting their chances to qualify for new loans. Conversely, several studies have shown that gains in home equity have a significant influence on the propensity to refinance, including, among others, Becketti and Morris (1990), Monsen (1992), Caplin, Freeman and Tracy (1993) and Krishnamurthy, Gabaix and Vigneron (2004). According to survey evidence reported in Canner, Dynan and Passmore (2002), 45% of homeowners who refinanced their mortgages in 2001 and early 2002 used the opportunity to extract equity. In summary, if house price movements affect mortgage prepayment in these and other ways, then any MBS pricing model that omits house prices as a state variable is misspecified.
A related issue is that the effects of mortgage defaults on MBS prices have received much less attention from both practitioners and the academic literature (notable exceptions in the literature include Kau et al. (1992, 1995), Schwartz and Torous (1992, 1993), Kau (1995), Deng, Quigley and Van Order (2000)). There are two basic reasons for the focus on prepayment rather than default. First, it is well known that defaults are generally rare events, given that most MBS are backed by first-lien mortgages protected by homeowner equity equal to 20% of the mortgage principal (80% loan-to-value ratio). Second, the bulk of residential MBS carry a credit guarantee from Ginnie Mae, a federal government agency, or either Freddie Mac or FannieMae, government-sponsored enterprises generally perceived to have the implicit backing of the federal government. Hence, for the bulk of MBS, the effect of mortgage defaults is to shift the return of principal forward in time, much like prepayments, and given the low incidence of defaults over recent history, a reasonable prior would seem to be that mortgage default can be ignored when modeling MBS.
In this article, we attempt to overcome both of these problems by developing and empirically estimating a structural two-factor mortgage valuation model that incorporates both interest rates and house prices as state variables. The structural approach has the potential to deliver a model that can produce informative forecasts in economic environments unlike those seen in the past, because mortgage terminations are the result of optimizing behavior by the agents in the model. Second, to the extent that overall terminations are correlated with house price movements, by incorporating house prices as a factor the model should more accurately describe termination behavior. The model explicitly values a borrower's joint option to prepay or default on his or her mortgage, thus allowing house price movements to affect both prepayment and default, and hence MBS prices. The model also incorporates discrete-time decision making on the part of borrowers and borrower-level heterogeneity in transaction costs, thereby capturing the well-known "seasoning" and "burnout" patterns observed in the termination behavior of home mortgages.
We estimate the parameters of the model using comprehensive data on termination rates for the mortgage pools backing Freddie Mac Participation Certificates issued between 1991 and 2002. The results indicate that house prices play a significant role in determining MBS prices. Specifically, when the two-factor model is compared to the nested one-factor interest-rate model (similar to that in Stanton (1995)), we find that the two-factor model produces a significantly better fit to the observed termination behavior of the pools. In addition, predicted MBS prices are closer to observed prices. We also use the model to examine the sensitivity of predicted MBS prices to movements in interest rates and house prices. This analysis indicates that, while MBS prices are primarily sensitive to interest rate fluctuations, house price movements also have an important effect. Movements in the value of the default option have a significant effect on the value of a mortgage borrower's prepayment option, and hence on the likelihood of prepayment. These results have important implications for hedging. In particular, even a strategy of hedging an MBS position against interest rate risk alone needs to take into account the fact that the optimal hedge ratio will vary substantially with the level of house prices.
The article is organized as follows. The next section reviews the existing valuation literature. The third section introduces the pool-level pricing model and the fourth section discusses how we implement the model. The fifth section describes the Freddie Mac data used in estimating the model, and the sixth discusses our estimation strategy and our results. The seventh section presents our pricing results and sensitivity analysis, and the final section concludes.
Pricing Mortgages
A fixed-rate home mortgage is a callable, defaultable bond whose payments are made by an individual borrower to a bank or other financial institution. Although many different mortgage types exist, we will focus on 30-year, fixed-rate mortgages--the loans backing most MBS. We will use the notation [B.sub.t] to denote the market value of the remaining scheduled payments in the absence of any options; we refer to this stream of payments as the "underlying bond." Valuing a mortgage amounts to valuing this bond together with its embedded options.
Prepayment
At any time after taking out the mortgage, the borrower may choose to stop making the remaining scheduled payments, and instead pay off the remaining principal amount, [F.sub.t]. (4) Paying off the loan is equivalent to exercising a call option on the bond [B.sub.t], with an exercise price equal to [F.sub.t]. Under a one-factor interest-rate model, the lower current interest rates are, the higher [B.sub.t] is, and hence the more in the money the prepayment option is. In a two-factor setting, movements in both interest rates and house prices determine the extent to which the option is in the money. When interest rates and house prices reach a boundary--the exact location of which is determined empirically for a reduced form model, or endogenously as part of the solution to the pricing problem for a structural model--the borrower exercises the option and pays off the loan early.
Default
In addition to choosing whether to make the scheduled monthly payment or to pay off the loan in full, a borrower may choose to default on the loan, handing over the house, the value of which we denote by [H.sub.t], and stopping all future mortgage payments. This default option is another call option on [B.sub.t], this time with exercise price [H.sub.t]. All else equal, the lower is [H.sub.t], the more attractive exercise of the default option is. However, it is important to emphasize that the default and prepayment options are not independent of one another. Because exercise of one option precludes exercise of the other, the options are substitutes, and movements in the value of one affect the value of the other. Hence the borrower holds a joint option to terminate the mortgage at any time by either prepaying or defaulting.
Background Terminations
Prepayments and defaults can occur for reasons unrelated to interest rate and house price movements. For example, a borrower might prepay a loan after deciding to move to a different house. Default might occur following an uninsured event that damages the house. The possibility that these types of "background" terminations might occur affects the value of the joint option both directly and indirectly. The direct effect is that the joint option might be exercised when it would not be optimal if the decision were based solely on interest rates and house prices. The indirect effect is through a change in the optimal exercise policy for the...
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